Question

Complete the input-output table for the function f(x) = (x−2)2+3
(2 points)
x f(x)
1 f(1)=

4 f(4)=

Answer 1

To complete the input-output table for the function \( f(x) = (x - 2)^2 + 3 \), we will calculate \( f(1) \) and \( f(4) \).

1. For \( f(1) \):
\[
f(1) = (1 - 2)^2 + 3
\]
\[
= (-1)^2 + 3
\]
\[
= 1 + 3
\]
\[
= 4
\]
So, \( f(1) = 4 \).

2. For \( f(4) \):
\[
f(4) = (4 - 2)^2 + 3
\]
\[
= (2)^2 + 3
\]
\[
= 4 + 3
\]
\[
= 7
\]
So, \( f(4) = 7 \).

Now, we can complete the input-output table:

\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
1 & 4 \\
\hline
4 & 7 \\
\hline
\end{array}
\]